Approximate solution of nonlinear hyperbolic equations with homogeneous jump conditions

Abstract

We present the error analysis of class of second order nonlinear hyperbolic interface problem where the spatial and time discretizations are based on finite element method and linearized backward difference scheme respectively. Both semi discrete and fully discrete schemes are analyzed with the assumption that the interface is arbitrary but smooth. Almost optimal convergence rate in \(H^1(\Omega)\)-norm is obtained. Examples are given to support the theoretical result.